Most chemical reactions are accelerated by an increase in temperature. The temperature dependence of the rate of a chemical reaction is explained by the Arrhenius equation
\[k = A\,e^{-E_a/RT}\]
where \(A\) is the Arrhenius factor (also called the frequency factor or pre-exponential factor) and \(E_a\) is the activation energy, expressed in J mol−1. A plot of ln \(k\) against \(1/T\) is a straight line with slope \(-E_a/R\). The rate constants \(k_1\) and \(k_2\) of a reaction at temperatures \(T_1\) and \(T_2\) are related as
\[\log\frac{k_2}{k_1} = \frac{E_a}{2.303R}\left[\frac{T_2 - T_1}{T_1T_2}\right]\]
For a chemical reaction, a rise in temperature by 10 K nearly doubles the rate constant, because the fraction of molecules having energy equal to or greater than the activation energy increases.
Identify the false statement from the following:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A reaction with a high activation energy proceeds rapidly when the temperature is lowered.
The passage states that most chemical reactions are accelerated by an increase in temperature, because the fraction of molecules with energy equal to or greater than Ea increases. Lowering the temperature does the reverse: fewer molecules reach Ea, k falls and the reaction becomes slower, not faster.
Option (1) Threshold energy is the minimum energy that colliding molecules must possess for their collision to form products. — A true statement. Only collisions with at least the threshold energy (and proper orientation) are effective and give products.
Option (2) Activation energy is the difference between the threshold energy and the energy possessed by the reacting species. — A true statement. Threshold energy = activation energy + energy possessed by the reacting species, so Ea is the difference.
Option (3) A catalyst increases the rate of a reaction by providing an alternate path of lower activation energy. — A true statement. A lower Ea means a larger fraction of molecules can react, so the rate rises.
Option (4) A reaction with a high activation energy proceeds rapidly when the temperature is lowered. — A false statement. A fall in temperature slows a reaction, and a high Ea already makes it slow.